Figure Captions

Fig. 1 Wave dispersion surfaces for the ring
dispersion. Four models are present when both a hot and cold electron
component are included.

Fig. 2. Concatenated dispersion surfaces
with their corresponding growth rates. The four dispersion surfaces
shown in Figure 1 have been merged into a
single display. We have truncated the surface identified with the
"cold intermediate" mode for reasons of clarity. An unstable mode is present
where two stable modes coalesce, and the corresponding growth rates are
shown by the contour plot.

Fig. 3. Solutions of the k = 0 shell
dispersion relation (6) for variable
/.
The left-handed column shows frequency while the right column shows the
corresponding growth rates. The integers inside and to the right of each panel give the j parameter of the DGH distribution. For
j >1,
/ j = 200.
When j = 0, both distributions are Maxwellian and we set
= 200. For the prupose of identifying modes, the solid line corresponds
to the "trapped" mode, the dashed line corresponds to the R-X
mode, and the dotted line corresponds to a Bernstein mode.

Fig. 8. Representative distribution functions for
which relativistic modifications are important. The plasma parameters
together with the corresponding solutions of the shell dispersion relation
for k = 0 are given as headers to each phase space density plot. The
dashed lines give the phase density of each electron species, with the sum
being given by the solid line. When obtaining solutions of the dispersion
relation, we have assumed that
/
= 0.01, and as can be seen
from the figure
/
j = 200 (p/mc =
0.1).